OF= 1

Let the side length of a square be x.

Because ∠ o = 45.

So OD=x

So OE=2x

Because of OE? +EF？ =OF？

So (2x)? +x？ = 1?

Solution: x=√5/5

So the side length of a square is √5/5.

Then subtract the area of triangle and square from the area of big fan.

Finally it should be equal to 1/8π-3/ 10.

(I wonder if there is any miscalculation)

(voiceover: ahem ... classmate, is "a difficult math problem in the senior high school entrance examination" exaggerated? -_-|||)